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Recap of Week 2

Based on the experiences of course leaders and students, we provide a summary of Week 2.
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Hello, it’s good to see you again. And, well, we finished the second week and I hope that you enjoyed the second week. I saw lots of comments beneath the items and it was very nice to see how you were engaging with the content. Of course we looked at Singapore and in Singapore we specifically looked at the Concrete- Pictorial-abstract approach and Bar Modeling. Many of you mention that they actually recognised a lot of these practices from their own schools and that’s very good to hear and indeed these principles are quite well-known.
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As I said before, Bruner started it in Western Europe already and they were then taken to Singapore, so if you recognise many of these principles and you’re already doing them, I would say, good for you! That’s great and maybe you can even adopt a couple of more of these principles. Another point that was made quite often is that in this course we keep it quite theoretical. So we’re really looking at the underpinnings, both from research but also the principles themselves.
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That was intentional: some people have said that it would be good to have some more concrete examples, which ironically fits very well in this Concrete-Pictorial-Abstract approach and I really encourage them to also look at the follow-up course which will be more practical. Nevertheless, I’ve taken one of the videos from this second course, about ‘the animal problem’ and I will provide a link in this step, so that you can actually have a look at some solutions for this ‘animal problem’. A final point I want to make is that some people noted that sometimes you don’t have to do the pictorial or the concrete phases, of course.
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If a student or a pupil is already really good at doing sums, multiplication sums for example, and you simply don’t need a pictorial approach, then okay that’s fine. They can just be very fluent in their multiplication sums. The whole point of this approach with multiple representations is that if you’ve got a challenging task you can actually fall back on these other representations. I think again this ‘animal problem’, because it’s actually quite a tricky problem if you don’t visualize it, could be very useful in demonstrating this. Okay, so we’re starting now with the third week. In this third week we’re going to look at China and Hong Kong. And we’re going to specifically look at the role that procedural knowledge has.
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Practice, practice makes perfect, sometimes people say, and also how it is inextricably related to conceptual knowledge. So procedural and conceptual knowledge go hand in hand. And then another point we’re going to look at is how you can actually sequence tasks in such a way, in a smart way, and that’s called using variation theory to actually improve both procedural and conceptual knowledge. So I hope you will enjoy the third week and I will see you in the comments.
Welcome to Week 3!
In Week 2 we focused on mathematics education in Singapore. Based on the experiences of Educators and learners, in this video we provide a summary of Week 2, and respond to some of the comments and questions made during the week.
In Week 3, we will move on to other Asian mathematics teaching methods. Singapore is not the only country that does well in international comparisons. Other East Asian countries and jurisdictions such as Japan, China and Hong Kong also excel.
This video was uploaded on Friday, the 14th of September, 2018 and is based on the comments made in the second run of the MOOC.
In the video I mention a video that is part of World Class Maths: Asian Teaching Practice. It shows how you could concretely work out the ‘animal problem’ with bar modeling in two different ways. The video is here
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World Class Maths: Asian Teaching Methods

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